Mathematical Models and Malaria

Chimezirim Evelyn Opara

Abstract

Malaria is amongst the leading causes of death in Africa alongside HIV/AIDS and remains endemic in Nigeria, whilst mostly affecting young children and pregnant women. With a population of 211.4 million, about 207,000 deaths from malaria are reported annually alongside 51 million diagnosed cases. Through subsequent research, I aim to find out if mathematical models can be created in order to assist the general population in understanding the extent to which the infection of malaria in pregnant women and the younger population can be regulated. As a result of this development, the paper measures the probability of ensuring the survival and successive reproductive rates, especially in developing countries without adequate funding or resources. 

Keywords: Malaria, Mathematical Models, Developing Countries

Employing the use of mathematical epidemiology to combat the prevalence of easily curable diseases in underrepresented communities

Diseases are a constant in society. Like a game of whack-a-mole, the creation of cures and elimination of particular diseases is counteracted with the development of new or mutated diseases. In the branch of epidemiology, researchers – otherwise known as epidemiologists – work to discern the causes of a disease, its spread, and possible methods to control the disease. The first step epidemiologists take to understand a disease is to obtain and analyze observed data from case studies/patients. Mathematical epidemiology employs the use of mathematical models to predict the progression of diseases and the effect that developed solutions have on the spread of that particular disease. More complex models also help researchers to analyze the outcome of public health intervention such as prohibiting in-person gatherings: like in the case of global quarantine instituted during the COVID-19 pandemic. 

Malaria is a disease caused by a plasmodium parasite that sucks the blood of humans and ingests disease-producing microorganisms into the blood of the hosts. It is amongst the leading causes of death in Africa alongside HIV/AIDS and remains endemic in Nigeria, my home country, whilst mostly affecting young children and pregnant women. With a population of 211.4 million, about 207,000 deaths from malaria are reported annually alongside 51 million diagnosed cases. 

In general, malaria is a curable disease if diagnosed and treated promptly. However, the insurgence of malaria in developing countries lacking adequate financial and health resources has resulted in the constant prevalence of malaria and rising death rates.

An approach to combat the spread and development of malaria in underperforming societies can be the development of mathematical models that simulate real world scenarios and provide solutions to problems. I yearn to understand if mathematical models can be developed to 

calibrate the impact of malaria in young children and pregnant women – the two groups most susceptible to this disease –  for a long term. My goal would be to create mathematical models that help us to understand the extent to which the infection of malaria in pregnant women and the younger population can be regulated in order to ensure survival and successive reproductive rates, especially in developing countries without adequate funding or resources. 

Ronald Ross was a British medical doctor who placed his main focus on developing preventive measures for the treatment and prevention of malaria in different parts of the world. Ross created a model that supported the theory that a reduction of the malaria-causing mosquito population below a certain level could be sufficient enough to control malaria. 

Mathematical Model Developed by Ronald Ross

However, a key factor that Ross’ model failed to encompass was the limit that the mosquito population was meant to be reduced to ; is this number situational and can it change based on environment and weather condition? Additionally, Ross also failed to include the extent to which it can affect  a population’s age structure – with a specific target on younger and middle aged groups. Also, would a reduction in the mosquito population size have an effect on the  biological diversity of an environment? Can one use existing representations like Ross’s to create new mathematical models that substantially serve as a basis for innovations that specifically work to maintain biological equilibriums and factors of population size like age structure?

Women and young children have continually remained the two demographics most susceptible to the malaria-causing plasmodium parasite. Children are vulnerable to malaria due to the fact that they have not developed enough immunity that helps them to defend themselves. Once the plasmodium parasite infects a child, it begins to multiply exponentially, eventually destroying red blood cell count in the body. As a result, vomiting, diarrhea, anemia, and fever ensue and begin to plague the medical victim. Pregnant women have a higher risk of infection due to changes in hormonal levels and the body’s immune system. Additionally, pregnant African women and children are more susceptible to malaria due to weather conditions that facilitate transmission and the socio-economic instability of the developing countries that causes an inability to financially control the spread of the malarial disease. Malaria during pregnancy can be harmful to both the mother and unborn child. Placental malaria in pregnant women leads to premature birth and low-birth weight. 

Additionally, low birth weight is also a major cause of neonatal mortality, a leading cause of death in Nigeria and other developing countries. Researchers report that about 75,000 to 200,000 global infant deaths occur annually due to malaria infection during pregnancy.

More than half of the deaths attributed to malaria are in children under 5 due to weaker immune systems. Oftentimes, diseases are spread amongst children due to close contact with children of similar ages(children with equally weak immune systems). Although malaria is not a contagious disease, its symptoms which include cough, vomiting and diarrhea can easily lead to other infections if not treated under sanitary conditions which is often the case in most developing African countries. Additionally, due to an inability to properly treat malaria. Most individuals in countries plagued by malaria often suffer a re-infection. As a result, severe anemia  and nephrotic syndrome – a chronic kidney disease – may develop. This condition can be found mostly in children in the tropic African region.

In some cases of this disease, neurological defects may develop as a result of a condition known as cerebral malaria. This occurs mostly in children and causes defects such as trouble with movement, palsies, speech difficulties(aphasia or apraxia), deafness and blindness when left untreated. 

It is strongly possible that innovations can be implemented to monitor the health of young children and mother’s in order to ensure health and wellbeing? Developing countries are unable to keep up with the spread of malaria due to a lack of resources. The prevention of malaria starts with providing clean water resources and hygienic environments necessary for survival. With further research, my goal is to develop low-cost systems that accommodate the economic situation in developing countries but help to maintain the wellbeing of young children and women.

References

Fred Brauer, F. B., & Abstract. We give a brief outline of some of the important aspects of the development of mathematical epidemiology. (2017, February 4). Mathematical epidemiology: Past, present, and future. Infectious Disease Modelling. Retrieved February 28, 2023, from https://www.sciencedirect.com/science/article/pii/S2468042716300367 

Dawaki, S., Al-Mekhlafi, H. M., Ithoi, I., Ibrahim, J., Atroosh, W. M., Abdulsalam, A. M., Sady, H., Elyana, F. N., Adamu, A. U., Yelwa, S. I., Ahmed, A., Al-Areeqi, M. A., Subramaniam, L. R., Nasr, N. A., & Lau, Y.-L. (2016, July 8). Is Nigeria winning the battle against malaria? prevalence, risk factors and KAP assessment among hausa communities in Kano State. Malaria journal. Retrieved February 28, 2023, from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4938925/#:~:text=Nigeria%20suffers%20the%20\

world’s%20greatest,risk%20of%20infection%20%5B5%5D. 

Centers for Disease Control and Prevention. (2022, March 22). CDC – malaria – about malaria – disease. Centers for Disease Control and Prevention. Retrieved February 28, 2023, from https://www.cdc.gov/malaria/about/disease.html 

Centers for Disease Control and Prevention. (2021, December 16). CDC – Malaria – malaria worldwide – impact of malaria. Centers for Disease Control and Prevention. Retrieved February 28, 2023, from https://www.cdc.gov/malaria/malaria_worldwide/impact.html#:~:text=Africa%20is

%20the%20most%20affected,cause%20severe%20malaria%20and%20death. 

Mandal, Sandip, et al. “Mathematical Models of Malaria – A Review – Malaria Journal.” BioMed Central, BioMed Central, 21 July 2011, https://malariajournal.biomedcentral.com/articles/10.1186/1475-2875-10-202.